(3*x + 5)*tan(x)
(3*x + 5)*tan(x)
Apply the product rule:
; to find :
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
The derivative of the constant is zero.
The result is:
; to find :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
The result is:
Now simplify:
The answer is:
/ 2 \ 3*tan(x) + \1 + tan (x)/*(3*x + 5)
/ 2 / 2 \ \ 2*\3 + 3*tan (x) + \1 + tan (x)/*(5 + 3*x)*tan(x)/
/ 2 \ / / 2 \ \ 2*\1 + tan (x)/*\9*tan(x) + \1 + 3*tan (x)/*(5 + 3*x)/